How do you tell? For example, cos(2x) has 3 options, so how do you know which to use?
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Human brains excel at pattern recognition.
Once you have done enough practice problems, you will become proficient at guessing the best choice. The answer is you use trial and error. Once you've explored the maze enough times, you'll get pretty good at going straight to the cheese.
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They technically can all be reversed; so, just like in a maze, you can always get from where you are to the cheese. But practically, usually you don't reverse a step, you start at an earlier step and choose a different way forward. [[ If I try cos(2θ) → 2cos²(θ)-1 and that doesn't seem to do it, I wouldn't reverse, it I'd just try something different with cos(2θ) (or an earlier step). ]] Generally, each conversion adds terms and get more and more complicated (and prone to error). So, when you come to a point where you think there is no way forward, you do not continue with the mash-up you have, you start over (or at least at an earlier place).
Once you have done enough practice problems, you will become proficient at guessing the best choice. The answer is you use trial and error. Once you've explored the maze enough times, you'll get pretty good at going straight to the cheese.
-=-
They technically can all be reversed; so, just like in a maze, you can always get from where you are to the cheese. But practically, usually you don't reverse a step, you start at an earlier step and choose a different way forward. [[ If I try cos(2θ) → 2cos²(θ)-1 and that doesn't seem to do it, I wouldn't reverse, it I'd just try something different with cos(2θ) (or an earlier step). ]] Generally, each conversion adds terms and get more and more complicated (and prone to error). So, when you come to a point where you think there is no way forward, you do not continue with the mash-up you have, you start over (or at least at an earlier place).
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You try the one which better matches with the situation.
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you try them all